Existence of three nontrivial solutions for a class of superlinear elliptic equations

On fractional plasma problems

“…, and a sequence (u j ) j ⊆ H l ⊕ H ⊥ m \ {0} such that (19) F µj (u j )ϕ = 0, for every ϕ ∈ H l ⊕ H ⊥ m and for every j ∈ N, and (20)…”

“…The proof of this result is obtained by using a critical point theorem of mixed nature proved in [11], already successfully applied in [13], [14], [15], [16], [18], [19], [31], [32], also for variational inequalities, see [9].…”

Existence and multiplicity results for the fractional Laplacian in bounded domains

“…Up to a subsequence, we can assume that λ n → λ in [λ i−1 + δ, λ j+1 − δ]. Choose z = u n in (15). Then, by (g 4 ) we obtain…”

Superlinear Perturbations of the Eigenvalue Problem for the Robin Laplacian Plus an Indefinite and Unbounded Potential

“…All the aforementioned works used the ARcondition to express the superlinearity of the perturbation f (z, •). A more general superlinearity condition was employed by Ou & Li [7] who also produced three nontrivial solutions for λ > 0 near a nonprincipal eigenvalue. As we have already mentioned earlier, there is no potential term in all the aforementioned works, and so the differential operator is coercive.…”